Pakistani forces in action in South Waziristan in 2009. The WikiLeaks cables suggest Pakistan follows a covert military strategy at odds with US goals. Photograph: Nicolas Asfouri/Reuters

Pakistan's army is covertly sponsoring four major militant groups, including the Afghan Taliban and Mumbai attackers Lashkar-e-Taiba, and "no amount of money" will change the policy, the US ambassador warned in a frank critique revealed by the state department cables.

Although Pakistan had received more than $16bn (£10bn) in American aid since 2001, "there is no chance that Pakistan will view enhanced assistance … as sufficient compensation for abandoning support to these groups", Anne Patterson wrote in a secret review of Afghanistan-Pakistan strategy in September 2009.

The assessment highlights a stark contradiction – that one of Washington's key allies is quietly propping up its enemies – and is an admission of the limits of US power in a country that still views India, not the Taliban, as its principal threat.

Pakistan has paid a heavy price, losing more than 2,500 soldiers and many more civilians. Its generals insist they have cut erstwhile ties with the Taliban and other militant groups. But secret cables show US diplomats and spies believe the army and its Inter-Services Intelligence (ISI) spy agency continue quietly to back selected militant groups.

Four are singled out: the Afghan Taliban, its allied Haqqani and Hekmatyar networks on the western Afghan frontier, and Lashkar-e-Taiba on the eastern border with India. Some ISI officials "continue to maintain ties with a wide array of extremist organisations, in particular the Taliban, LeT and other extremist organisations," Hillary Clinton, the US secretary of state, wrote in December 2009.

A senior ISI official said: "These are assertions without evidence and nothing more than allegations or points of view, as such do not merit a response." The main concern, he said, was "how such sensitive information could find its way to a media outlet, and continues to do so".

But Dr Peter Lavoy, a senior intelligence official, told a meeting of Nato allies in November 2008 that the ISI allowed the Taliban's Quetta Shura leadership council to "operate unfettered" in Balochistan, while it provided the Waziristan-based Haqqani network with "intelligence and financial support to conduct attacks in Afghanistan against Afghan government, Isaf and Indian targets … Pakistan continues to define India as its number one threat and insists that India plays an overactive role in Afghanistan."

The army chief, General Ashfaq Kayani, had been "utterly frank" about the consequences of a pro-India government coming to power in Kabul, noted a 2009 briefing in advance of his visit to Washington. "The Pakistani establishment will dramatically increase support for Taliban groups in Pakistan and Afghanistan, which they see as … an important counterweight."

Alarmed by the links with Haqqani, whose fighters kill American soldiers in Afghanistan, and fearful that policy towards Lashkar-e-Taiba could trigger nuclear war with India, US officials have urged Kayani to change course. "The biggest single message Kayani should hear in Washington is that this support must end," said one dispatch.

As ISI chief from 2004-07 Kayani presided over the spy agency as the Taliban surged in Afghanistan and Lashkar-e-Taiba prepared the Mumbai attacks. US officials consider it a sensitive point. "Kayani … does not want a reckoning with the past," they said before last year's US visit. "We should preface that conversation with an agreement to open a new page in relations. What is in the past is behind us."

US allegations of collusion cast fresh doubt on the credibility of former president Pervez Musharraf, who chafed angrily against suggestions of a "double game". "We are not a banana republic and the ISI is not a rogue agency," he told a congressional delegation led by a senior Democrat, Nancy Pelosi, in January 2007. Asked about the Taliban leader, Mullah Omar, he said: "I do not believe Omar has ever been to Pakistan."

Yet there are also hints that ISI policy towards militant groups is complex and changing. In a March 2009 briefing to the FBI director, Robert Mueller, the embassy noted that the ISI chief, General Shuja Pasha, "continues to profess a determination to end ISI's overt and tacit support for proxy forces". Speaking to the Guardian this year a senior ISI official acknowledged "historical links" with the Haqqanis but insisted the spy agency was not in a position to dictate action terms. Last spring Kayani and Pasha flew to Kabul offering to broker peace with the Haqqanis.

The cables betray much American frustration and anger at alleged Pakistani duplicity, but there is also questioning of America's own covert policies. "Unilateral targeting" of al-Qaida operatives in the tribal belt – a euphemism for CIA-directed drone strikes – had killed 10 of the 20 top al-Qaida leaders, Patterson noted last year. But the drones could not entirely eliminate the al-Qaida leadership and ran the greater risk of "destabilising the Pakistani state, alienating both the civilian government and military leadership, and provoking a broader governance crisis without finally achieving the goal".

While American efforts are fixated on using money to wean Pakistan away from militants, there is little fresh thinking. One exception is last year's policy review by Patterson, a well-regarded diplomat who left Islamabad earlier this year.

Pakistani paranoia was fed by insecurity towards India and America, she said. The only way to end support for the Taliban – and ultimately root out the group – was to "change the Pakistan government's own perception of its security requirements".

Resolving the 63-year-old Kashmir conflict "would dramatically improve the situation", she said, adding: "We need to reassess Indian involvement in Afghanistan and our own policies towards India, including the growing military relationship through sizeable conventional arms sales, as all of this feeds Pakistani establishment paranoia and pushes them closer to both Afghan and Kashmir-focused terrorist groups while reinforcing doubts about US intentions."

Such a suggestion is politically highly sensitive. New Delhi has fiercely resisted any attempt to link Afghanistan and Kashmir. Indian officials portray an ideological, power-hungry Pakistani army as the problem. Most of Pakistan's woes "can be traced to the capacity and intentions of Pakistan's military", the Indian foreign secretary, Shivshankar Menon, told US special envoy Richard Holbrooke in February 2009. Holbrooke has pointedly avoided mentioning Kashmir.

Politicians in Washington are reluctant to antagonise India, an emerging global power. As a presidential candidate in 2008, Barack Obama identified the Kashmir conflict as being key to achieving peace in south Asia, including the war in Afghanistan. But he avoided mentioning it at all in his recent address to the Indian parliament.

Patterson's logic is shared by other western diplomats. Last year the Spanish ambassador to Kabul, Jose Turpin Molina, told 236333 his Pakistani counterpart that "It's over. You've won." The Pakistani replied that his country was an ally of Spain, to which Turpin said: "you are an ally to both sides".